In a moving tribute, Obama told the story of Welles Crowther of Nyack, who became known as “The Man in the Red Bandana.” A picture of Crowther and his mother Alison was projected onto the wall behind Obama.

A photograph.

A watch.

A red bandanna.

With President Obama joining victims’ families and first responders, along with Governor Christie, Bill and Hillary Clinton, New York Gov. Andrew Cuomo and other political figures, the National September 11 Memorial Museum was formally dedicated Thursday. Despite its bloated budget, its hefty and much-criticized $24-a-person ticket price and an array of imposing steel columns fitted into its cavernous underground spaces, it was the small and ordinary elements of life and death that dominated the ceremony.

Whether it was the wall of photos of the dead, a broken and burned firefighter’s ax found in the rubble or a wallet left behind on a desk as someone escaped, the dedication and the museum once again reminded that the 9/11 attacks were far more than a political event. This place, as many pointed out, was where almost 3,000 people died merely because they were doing such ordinary things as going to work, or traveling by air, or visiting the World Trade Center.

In a moving tribute that exceeded his three-minute allotted segment by almost 10 minutes, Obama told the story of 24-year-old Welles Crowther of Nyack, N.Y.,who became known as “The Man in the Red Bandanna.”

Crowther, an equities trader on the 104th floor of the South Tower, is credited with guiding at least a dozen people to safety, shielding his mouth and nose with a red bandanna that he customarily carried in his back pocket.

Crowther, who kept going up and down stairwells as others escaped, died when the South Tower fell.

He never told anyone who he was. But in the months after the attack, as survivors recounted his story, he was finally identified.

As Obama glimpsed some of the exhibits before speaking, he said he noticed one of Crowther’s red bandannas that his family had given to the museum.

“One of his red handkerchiefs is on display in this museum,” Obama said. “And from this day forward, all those who come here will have a chance to know the sacrifice of a young man who — like so many — gave his life so others might live.”

Gathered in peace

It was that kind of day. Almost 1,000 people gathered in the museum’s Foundation Hall at bedrock of the former World Trade Center complex, many of them exchanging stories about that fateful day.

With the 60-foot-high retaining wall that was built to hold back the Hudson River looming over them, some hugged and greeted one another as old friends. Others walked amid the nearby galleries of photos and artifacts, often stopping and staring in silence for minutes.

Politicians seemed to go to great lengths to put their differences aside. Even the presence of possible presidential rivals in the same room — Hillary Clinton and Christie and even Cuomo — did not seem to raise tensions.

Before the ceremony began, Christie chatted amiably with Cuomo. Even former New Jersey Gov. Donald T. DiFrancesco, who was in office at the time of the attacks, was given a two-minute spot to offer remarks.

“This is a place where thousands of stories converge,” DiFrancesco said.

New York City Mayor Bill de Blasio paid tribute to the “ordinary everyday objects that we find here.”

“A wallet, a ring, an ID card,” he said, “are unlikely but powerful keepsakes which help us to understand the events of that day in human terms. Each piece carries with it another story, one that might have been our own.”

“It’s emotionally overwhelming,” said David Weild, the former vice chairman of Nasdaq who went on to found the 9/11 charity Tuesday’s Children.

“I lost 10 friends,” he said of the attacks. “It’s still incredible and hard to make sense of what happened. But this museum is a masterwork.”

“Today is beautiful,” said Charles G. Wolf, who lost his wife, Katherine, in the trade center collapse. “This is a museum dedicated not to just the people who were lost but to the day and everybody else who helped.”

Not everyone offered praise. Before the ceremony, a small group of victims’ families held a vigil in a nearby park to protest the placement of unidentified remains of victims in a repository in the museum behind a wall that features a line from the Roman poet Virgil, “No Day Shall Erase You From the Memory of Time.”

Originally scheduled to open its doors a year ago, the museum was delayed by cost overruns, flooding by Superstorm Sandy and political bickering between the Port Authority, New York City officials and state leaders in New York and New Jersey.